Math Problem Statement

Find the angle correct to two decimal places for the lines joining the given points that they make with the positive direction of the x-axis

Solution

To find the angle that a line joining two points makes with the positive xx-axis, we use the slope of the line and the relationship between slope and angle.

Formula:

The slope of a line is given by: m=y2y1x2x1m = \frac{y_2 - y_1}{x_2 - x_1} The angle θ\theta that the line makes with the positive xx-axis is then calculated using: θ=tan1(m)\theta = \tan^{-1}(m) where θ\theta is measured in radians or degrees. Ensure the angle is in the correct quadrant based on the signs of (x2x1)(x_2 - x_1) and (y2y1)(y_2 - y_1).


Steps:

  1. Compute the slope mm using the coordinates of the two points.
  2. Use the inverse tangent function to find the angle θ\theta in radians or degrees.
  3. Adjust θ\theta to ensure it is in the correct quadrant.
  4. Round θ\theta to two decimal places.

Example Input:

Please provide the two points (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2), and I will calculate the angle for you.

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Math Problem Analysis

Mathematical Concepts

Geometry
Trigonometry
Slope
Coordinate Geometry

Formulas

m = (y2 - y1) / (x2 - x1)
theta = tan^(-1)(m)

Theorems

Inverse Tangent Function
Slope-Angle Relationship

Suitable Grade Level

Grades 9-12